Effects of local wall thinning on plastic limit loads of elbows using geometrically linear FE limit analyses

This paper provides closed-form plastic limit load solutions for elbows under in-plane bending and internal pressure, via three-dimensional (3D), geometrically linear FE limit analyses using elastic-perfectly plastic materials. Wide ranges of elbow and thinning geometries are considered. To investigate the effect of the axial thinning length on limit loads systematically, two limiting cases are considered; a sufficiently long thinning, and the circumferential part-through surface crack. Closed-form plastic limit load solutions for wall thinning with intermediate longitudinal extents are then obtained from these two limiting cases. The effect of the axial extent of wall thinning on plastic limit loads for elbows is highlighted by comparing that for straight pipes. Although the proposed solutions are developed for the case when wall thinning exists in the center of elbows, it is also shown that they can be applied to the case when thinning exists anywhere within the elbow.     

Finite element limit analyses of under-matched tensile specimens

This paper quantifies the effect of under-matching on plastic limit loads and fully plastic stress triaxialities for mismatched flat plate (in plane strain and plane stress) and round bar tensile specimens, via parametric finite element (FE) limit analyses based on elastic-perfectly-plastic materials. It is found that the effect of the strength mismatch ratio (the ratio of the yield strength of the weld zone to that of the base material) on plastic limit loads and fully plastic stress triaxialities can be significant for plane strain plate and round bar specimens, but much less significant for plane stress plate specimens. Its effect is dependent significantly on the slenderness of the weld zone (defined by the ratio of the weld zone width to the specimen width). The effect of the slenderness of the weld zone is apparent only when the weld width is less than the specimen width or diameter. In particular, the stress triaxiality in the softer weld zone can increase significantly with decreasing the ratio of the weld zone width to the specimen width (radius). Based on the present limit load results, a simple method to extract intrinsic tensile properties of the under-matched weld zone from test results of under-matched tensile specimens is proposed.     

Plastic limit loads for cracked large bore branch junction

This paper reports plastic limit loads for a cracked large bore branch junction, based on three-dimensional finite element limit analyses using elastic-perfectly plastic materials. Part-through surface and through-wall cracks are postulated in the intersection. For loading conditions, internal pressure and (in-plane and out-of-plane) bending to the branch pipe and to the run pipe are considered. The effect of the crack on limit loads is found to be significant for internal pressure and bending to the branch pipe, but not for bending to the run pipe. The large geometry change effect for bending to the branch pipe is briefly discussed.     

A new finite element for buckling analysis of laminated stiffened plates

A new stiffened plate element for stability analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and a Discrete Kirchhoff–Mindlin plate bending element. The element includes transverse shear effects. The model accommodates any number of arbitrarily oriented stiffeners within the plate element and eliminates constraints on the mesh division of the plate. The element has no problem associated with shear locking – a phenomenon usually encountered in isoparametric elements. The stability analysis of laminated stiffened plates has been carried out under different loading conditions with the present element.     

A semi-analytical finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for laminated composite plates. The method is based on a mixed variational principle that involves both displacements and stresses. Finite element meshes are only used in the plane of plate, while the through thickness distributions of displacements and stresses are obtained using the method of state equations. Numerical results show that the rate of convergence of the new method is fast and the solutions can be very close to corresponding exact three-dimensional ones. The use of a recursive formulation of the state equations leads to an algebra equation system, from which solution are sought, whose dimension is independent of the numbers of layers of the plate considered.     

An adaptive remeshing procedure for discontinuous finite element limit analysis

An adaptive remeshing procedure is proposed for discontinuous finite element limit analysis. The procedure proceeds by iteratively adjusting the element sizes in the mesh to distribute local errors uniformly over the domain. To facilitate the redefinition of element sizes in the new mesh, the interelements discontinuous field of elemental bound gaps is converted into a continuous field, ie, the intensity of bound gap, using a patch‐based approximation technique. An analogous technique is subsequently used for the approximation of element sizes in the old mesh. With these information, an optimized distribution of element sizes in the new mesh is defined and then scaled to match the total number of elements specified for each iteration in the adaptive remeshing process. Finally, a new mesh is generated using the advancing front technique. This adaptive remeshing procedure is repeated several times until an optimal mesh is found. Additionally, for problems involving discontinuous boundary loads, a novel algorithm for the generation of fan‐type meshes around singular points is proposed explicitly and incorporated into the main adaptive remeshing procedure. To demonstrate the feasibility of our proposed method, some classical examples extracted from the existing literary works are studied in detail.     

Finite element plastic loads for circumferential cracked pipe bends under in-plane bending

This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic-perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.     

Extended finite element method for plastic limit load computation of cracked structures

The extended finite element method is extended to allow computation of the limit load of cracked structures. In the paper, it is demonstrated that the linear elastic tip enrichment basis with and without radial term may be used in the framework of limit analysis, but the six‐function enrichment basis based on the well‐known Hutchinson–Rice–Rosengren asymptotic fields appears to be the best. The discrete kinematic formulation is cast in the form of a second‐order cone problem, which can be solved using highly efficient interior‐point solvers. Finally, the proposed numerical procedure is applied to various benchmark problems, showing that the present results are in good agreement with those in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

A finite element analysis of cracked square plates and bars under antiplane loading

ABSTRACT Finite element analyses were carried out on cracked 20 mm square plates and bars ranging in thickness from 2.5 mm to a length of 60 mm. The crack extended from the middle of one side of the square to its centre, and was modelled as a narrow, parallel‐sided notch with a semicircular tip. An antiplane loading was applied to the side containing the crack. An infinitely long bar under the antiplane loading used is in pure Mode III. It was found that the central portions of 40, 56 mm and 60 mm long bars were in pure Mode III, and also that K_III was approximately constant. These central portions were therefore representative of an infinitely long bar. Towards the ends of a bar K_III decreased. At the ends of a bar corner point effects meant that Mode II stress intensity factors and displacements were induced in the corner region. The size of the corner region was independent of bar length. In the 2.5, 5 and 10 mm thick plates out of plane bending means that the antiplane loading became a mixed Mode II and Mode III loading. At a centre line K_II is zero by symmetry. Behaviour in the corner region was a function of plate thickness. For both plates and bars, as has been predicted theoretically, the ratio K_II/K_III tends to a constant value as a surface is approached. For a thickness of 20 mm, that is a 20‐mm cube, behaviour represents a transition between plate and bar behaviour.     

Quantification of the yield strength-to-elastic modulus ratio effect on TES plastic loads from finite element limit analyses of elbows

This paper quantifies the effect of the yield strength-to-elastic modulus ratio on twice-elastic-slope plastic loads for 90-degree elbows under in-plane and out-of-plane bending. Based on extensive and systematic finite element limit analyses using elastic-perfectly plastic materials, simple regression equations between the yield strength-to-elastic modulus ratio and twice-elastic-slope plastic loads for elbows under in-plane closing, in-plane opening and out-of-plane bending are proposed, and validated against published experimental data. Applicability of the proposed equations to circumferential cracked elbows under in-plane bending is also investigated.     

Computations of the stress intensity factors of double-edge and centre V-notched plates under tension and anti-plane shear by the fractal-like finite element method

The fractal-like finite element method (FFEM) is extended to compute the stress intensity factors (SIFs) of double-edge-/centre-notched plates subject to out-of-plane shear or tension loading conditions. In the FFEM, the use of global interpolation functions reduces the large number of unknowns in a singular region to a small set of generalised co-ordinates. Therefore, the computational cost is reduced significantly. Also, neither post-processing techniques to extract the SIFs nor special singular elements are needed. Many numerical examples of double-edge-/centre-notched plates are presented, and results are validated via existing published data. New results of notched plate problems are also introduced.     

Cone bit bearing seal failure analysis based on the finite element analysis

Failure analysis of cone bit bearing seals is important in reducing production cost and preventing in-service component failure. However, a generally accepted criterion for their failure has not yet been established because of complexities in both their material properties and the environment. In this study, a two-dimensional axisymmetric finite element analysis (FEA) numerical model was established. FEA software was developed based on the Mooney–Rivlin constitutive model of the rubber material, and the penalty function contact algorithm. The distributions of stress, strain and contact pressure were analyzed to establish their effect on failure. The locations and causes of the failure and preventive measures were determined by comparison with an actual failure case. It was found that stress concentration and uneven pressure distribution occur at the seal. Rubber rings are highly and unequally compressed. Metal ring structure mainly determines sealing performance. To reduce the occurrence of failure, the structure must be improved by: designing an appropriate angle-tapered metal ring end face structure instead of a plane to change the trend in pressure distribution, increasing the contact area of the metal ring end face to reduce contact pressure and make the contact pressure distribution more uniform to reduce sealing surface wear, reducing the radial thickness to reduce the compression of the rubber ring, and improving back support structures to reduce the stress concentration. Results from the study can prevent and minimize risk for future failures to increase bit life and reduce drilling costs.     

Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP

Strengthening of steel structures using externally-bonded carbon fibre reinforced polymers ‘CFRP’ is a rapidly developing technique. This paper describes the behaviour of axially loaded flat steel plates strengthened using carbon fibre reinforced polymer sheets. Two steel plates were joined together with adhesive and followed by the application of carbon fibre sheet double strap joint with different bond lengths. The behaviour of the specimens was further investigated by using nonlinear finite element analysis to predict the failure modes and load capacity. In this study, bond failure is the dominant failure mode for normal modulus (240 GPa) CFRP bonding which closely matched the results of finite elements. The predicted ultimate loads from the FE analysis are found to be in good agreement with experimental values.     

Plastic limit analysis of cylindrically orthotropic circular plates

The plastic limit analysis of cylindrically orthotropic circular plates is developed using a piecewise linear orthotropic yield criterion. The yield criterion is a modification of an isotropic formulation that consists of a series of weighted piecewise linear components. The piecewise linear yield criterion enables an analytical solution for the plastic limit load of cylindrically orthotropic circular plates. Plastic limit analysis for both simply supported and clamped circular plates under uniformly distributed load are carried out. Parametric studies are conducted to investigate the sensitivity of the plastic limit loads to material orthotropy and influences of orthotropic ratio and chosen yield criteria on the plastic limit loads of the circular plates are discussed. It is found that the plastic limit loads of the orthotropic circular plates are affected significantly by the orthotropic ratio. Enhancement of the circumferential yield moment will increase dramatically the plastic limit load of the plates. Moment and velocity fields of the plates in plastic limit state are also derived and discussed. The results obtained from the present study are helpful in understanding the failure mechanism of orthotropic circular plates and is useful for design.     

Ballistic limit for oblique impact of thin sandwich panels and spaced plates

Ballistic perforations of monolithic steel sheets, two-layered sheets and lightweight sandwich panels were investigated both experimentally and numerically. The experiments were performed using a short cylindrical projectile with either a flat or hemispherical nose that struck the target plate at an angle of obliquity. A total of 170 tests were performed at angles of obliquity 0–45°. The results suggest that during perforation by a flat-nosed projectile, layered plates cause more energy loss than monolithic plates of the same material and total thickness. There was no significant difference in the measured ballistic limit speed between monolithic plates and layered plates during oblique impact perforation by a hemispherical-nosed projectile.     

Boundary element frequency domain formulation for dynamic analysis of Mindlin plates

A new boundary element formulation for analysis of shear deformable plates subjected to dynamic loading is presented. Fundamental solutions for the Mindlin plate theory are derived in the Laplace transform domain. The characteristics of the three flextural waves are studied in the time domain. It is shown that the new fundamental solutions exhibit the same strong singularity as in the static case. Two numerical examples are presented to demonstrate the accuracy of the boundary element method and comparisons are made with the finite element method. Copyright © 2006 John Wiley & Sons, Ltd.     

A stabilized discrete shear gap finite element for adaptive limit analysis of Mindlin–Reissner plates

This paper presents a numerical formulation for computation of collapse load of Mindlin–Reissner plates that uses stabilized discrete shear gap finite elements and second‐order cone programming. Displacement fields are approximated using the discrete shear gap in combination with a stabilized strain smoothing technique, ensuring that shear‐locking problem can be avoided and that accurate solutions can be obtained. The underlying optimization problem is formulated in the form of a standard second‐order cone programming, so that it can be solved using highly efficient primal‐dual interior‐point algorithm. An error indicator based on plastic dissipation will be used in the adaptive refinement scheme. Various plates with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparative study of finite element based response evaluation methods for laminated plates

In this paper, four methods for the through the thickness response evaluation of laminated composite and sandwich plates are comparatively evaluated in terms of their characteristics and numerical accuracy. The laminated composite and sandwich plates are subjected to thermo-mechanical loading. The four methods include two post-processor-type methods and two re-analysis-type methods. The post-processor-type methods based on the three-dimensional stress equilibrium equations and the three-dimensional thermo-elasticity equations. And the re-analysis methods are based on the incorporation of the nonlinear through the thickness displacements recovered using post-processing technique in the re-analysis phase. The accuracy of the proposed methods for the evaluation of the through the thickness responses of the laminated plates are assessed via numerical examples of various configurations of laminated plates. Also, applicability and computational efficiencies of the methods are discussed. This research was supported in part by a grant from the BK-21 program for Mechanical and Aerospace Engineering Research at Seoul National University. The authors also gratefully acknowledge the financial support from the Ministry of Science and Technology through the National Laboratory Programs.     

Finite element analysis using interfragmentary strain theory for the fracture healing process to which composite bone plates are applied

The present paper deals with finite element analyses to estimate the healing efficiency of fractured long bones to which various composite bone plates are applied. To estimate the callus modulus according to the healing period, interfragmentary strain theory was used, and the iterative process for updating the newly determined callus properties in every finite element was implemented by a user-defined sub-routine constructed by the Python code. The results of analysis revealed that a composite bone plate made of a plain weave carbon/epoxy composite whose Young’s modulus was in the range of 30–70 GPa produced a positive effect on the healing efficiency relieving stress-shielding effect. This result can be used in the detailed design of high-performing composite bone plates to determine more effective shapes and stacking sequences for better healing efficiency.